T.R. would curbstomp Champ Clark and handily beat W.W. in a general election. As for what happens next, I suppose Roosevelt spends the first two years of his presidency trying to move the nation into the war, as his cousin did with WWII IOTL. Wilson or whoever can run as an anti-war candidate in 1916 and will probably lose handily again if the allies are doing well. If T.R. dies in 1919 as he did IOTL, V.P. Hiram Johnson or Charles Fairbanks becomes POTUS. If not, T.R. runs for a third term in 1920, and the Socialists start picking up the slack from the Democrats, who continue to decline, having not held the White House since the 1880s.
Assuming that T.R. lives and rides onto another term in the White House, he probably becomes even more the stuff of legend than he is IOTL. Re-elected in 1924 before turning over the reigns of government to a new generation, retiring to his historiography and hunting. The Republicans keep the White House until 1932, when the Socialist Party has its big break, and takes over, with the Democrats becoming a rural, Southern-based party with nearly no northern representatives.